Absolutely not. You won't get alcohol.
Here's the science. What yeast does is feed on the sugar and starch in the ingredients, and convert them roughly half to alcohol and half to carbon dioxide gas. Which the yeast excretes. Yeast is a living organism, a microscopic fungus, so this is a biological process and nothing will substitute for it. (Are fungi animals or plants? They seem to be a bit of both so scientists prefer to put them in their own category! But to you and me, they're more like an odd kind of plant than anything. Vegans eat mushrooms - let's join them and say fungi are plants.)
Which is why it takes time to work. In bread, you want the gas to make it rise but not the alcohol, but that will boil off in the oven. If you're making alcohol, you want the opposite - you want the alcohol and to let the gas bubble off. Either way, it takes time for the yeast to munch away on sugar and produce its alcoholic pee and carbon dioxide farts. (Same as with your food - it gets through your body and what's left emerges in about 24 hours, but yeast does it MUCH faster.) So bread needs time to rise, and alcohol takes time to ferment.
In making alcohol, eventually the yeast will knock itself out or die from alcohol poisoning, or it runs out of food and dies of starvation. So you can make beer or wine just by fermenting the liquid, but if you want something stronger, you need to distil it. In distilling, alcohol boils off first because it boils at a lower temperature than water, you collect what boils off, and bingo, you have something stronger to drink. (It's also usually illegal to do this without a licence and that's the reason you want to keep making moonshine quiet! Our school chemistry lab had a distiller so we could make our own pure distilled water, but you COULD make moonshine in it so it needed a licence! Just remember the chemistry teacher mentioning it.)
Baking soda, on the other hand, works totally differently. The process is purely chemical. It's a mild alkali and as a bicarbonate, will react with anything acidic in the recipe to produce a chemical salt + water + carbon dioxide. So you'll get gas bubbles to make your mixture rise, and quite quickly too so you don't need to leave cake mixture to rise, but you will get no alcohol. If you want alcohol, gotta have yeast.
Just for fun, because in making bread it's the gas you want, you CAN make it with baking soda. If you want quick home-made bread, make soda bread. It doesn't use yeast and relies on baking soda and buttermilk. They'll get together in the dough, do that chemical reaction and you'll get risen bread. But no, it doesn't work the other way round when you want alcohol. Only yeast can do that.